Question

A beam of parallel light rays is incident on a solid transparent sphere of refractive index $\mu$ . If a point image is produced just at the back of the sphere, what is the refractive index of the sphere?

• A. 2.0
• B. 2.3
• C. 2.5
• D. 2.7

Answer 1

Answer: (A)

Let $C$ be the centre and $P_1$ and $P_2$ the poles of the sphere.
$A$ ray $OA$parallel to a diameter is first refracted into the glass along $AB$.
For refraction at $A$ from air to glass, we have
$\frac{\mu }{v}-\frac{1}{u}-\frac{\mu -1}{R}$
Here $u=\infty$
and $v=2R$
$\therefore \frac{\mu }{2R}-\frac{1}{\infty }=\frac{\mu -1}{R}$
$\frac{\mu }{2R}=\frac{\mu -1}{R}$
$\mu =2\mu -2$
$\mu =2$